1234567
of 7

Multiplying Matrices

Let's use these matrices:

A = [ row 1: -1 , 5 row 2: 2 , -3 ]

B = [ row 1: 0 , 9 row 2: 8 , -6 row 3: 4 , 7 ]

Let's find B times A :

I do these by stacking...  B times A ...

                                        A is [ row 1: -1 , 5 row 2: 2 , -3 ]

B is [ row 1: 0 , 9 row 2: 8 , -6 row 3: 4 , 7 ] ... place an empty matrix of size m x p next to matrix B and below matrix A

  

 

 

 

The answer goes here.

We just do an intersecting row and column thing:

A = [ row 1: -1 , 5 row 2: 2 , -3 ] ... B = [ row 1: 0 , 9 row 2: 8 , -6 row 3: 4 , 7 ] ... use column 1 of matrix A and row 1 of matrix B and see where they intersect in the answer matrix c  

Row 1 of B and column 1 of A intersect in entry c11 of the answer matrix...

 

A = [ row 1: -1 , 5 row 2: 2 , -3 ] ... B = [ row 1: 0 , 9 row 2: 8 , -6 row 3: 4 , 7 ] ... 18 goes in c11 of the answer matrix c  

 

To fill this spot, we multiply and add:

( 0 ) ( -1 ) + ( 9 ) ( 2 ) = 18